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A survey on sensor calibrationin air pollution monitoringdeployments

Journal Article

Author(s):Maag, Balz ; Zhou, Zimu ; Thiele, Lothar

Publication date:2018-12

Permanent link:https://doi.org/10.3929/ethz-b-000276449

Rights / license:In Copyright - Non-Commercial Use Permitted

Originally published in:IEEE Internet of Things Journal 5(6), https://doi.org/10.1109/JIOT.2018.2853660

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IEEE INTERNET OF THINGS JOURNAL, VOL. XX, NO. X, XXX 2018 1

A Survey on Sensor Calibration in Air PollutionMonitoring Deployments

Balz Maag, Member, IEEE, Zimu Zhou, Member, IEEE, and Lothar Thiele Member, IEEE

Abstract—Air pollution is a major concern for public healthand urban environments. Conventional air pollution monitoringsystems install a few highly accurate, expensive stations atrepresentative locations. Their sparse coverage and low spatialresolution are insufficient to quantify urban air pollution andits impacts on human health and environment. Advances in low-cost portable air pollution sensors have enabled air pollutionmonitoring deployments at scale to measure air pollution athigh spatiotemporal resolution. However, it is challenging toensure the accuracy of these low-cost sensor deployments becausethe sensors are more error-prone than high-end sensing infras-tructures and they are often deployed in harsh environments.Sensor calibration has proven to be effective to improve the dataquality of low-cost sensors and maintain the reliability of long-term, distributed sensor deployments. In this article, we reviewthe state-of-the-art low-cost air pollution sensors, identify theirmajor error sources, and comprehensively survey calibrationmodels as well as network re-calibration strategies suited fordifferent sensor deployments. We also discuss limitations ofexiting methods and conclude with open issues for future sensorcalibration research.

Index Terms—Sensor calibration, low cost sensors and devices,air pollution sensors, air quality sensor networks,

I. INTRODUCTION

URBAN air pollution affects the quality of life and publichealth. Pollutants such as particulate matter (PM), ozone

(O3), carbon monoxide (CO) or nitrogen dioxide (NO2) cancause respiratory illnesses or cardiovascular diseases. A studyby the World Health Organization estimated that 11.6% of allglobal deaths in 2012 can be traced back to air pollution [1].Heavily polluted air also leads to environmental problems suchas acid rain, stratospheric ozone depletion and global climatechange. Monitoring air pollution is of growing importance toincrease public awareness and involvement in human healthand sustainable urban environments [2].

Traditionally, air pollutants are monitored by fixed sites withexpensive high-end sensing infrastructure run by governmentalauthorities. These monitoring sites are usually distributedsparsely and only suffice to estimate the average pollutionaffecting large populations. However, air pollution is knownto be a complex phenomenon with sophisticated spatial andshort-term variations [3]. For instance, in major streets, thepollutant concentrations may vary within tens of meters and

The authors were with the Department of Information Technology andElectrical Engineering, ETH Zurich, Switzerland, e-mail: {bmaag, zzhou,thiele}@tik.ee.ethz.ch

Manuscript received March 3, 2018; revised June 21, 2018.Copyright (c) 2012 IEEE. Personal use of this material is permitted.

However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to pubs-permissions@ieee.org.

over time within minutes [4]. Therefore, it is desirable toincrease the spatiotemporal resolution of available air pollutioninformation for the public to assess their personal health risksand take precaution measures.

A driving factor that enables these increased monitoringefforts is the availability of low-cost portable air pollutionsensors. These sensors are usually small, consume low power,cost roughly between 10$ and 1′000$ and are able to measurethe concentrations of all the major air pollutants. Comparedto bulky high-end solutions (≥ 10′000$), low-cost sensorsare particularly convenient for large-scale static and mobiledeployments [5]–[8]. By now, low-cost air pollution sensorshave been successfully integrated into various long-term de-ployments to provide fine-grained air pollution information forquantitative studies and public services [9].

Unfortunately the data provided by these deployments isoften lacking sufficient accuracy [9], [10]. Many researchersreport about serious inaccuracies when comparing the low-costsensor measurements to reliable and accurate measurement ofconventional monitoring sites [11], [12]. The reason for thisunsatisfying performance can be linked to various limitationsof state-of-the-art low-cost sensors, such as low signal-to-noiseratios or interference from environmental factors [13], [14].

In order to improve the data quality of existing and futureair quality monitoring deployments, active research efforts aredevoted to counteract these limitations with appropriate sensorcalibration. By calibrating a low-cost sensor its measurementsare transformed in a way that the calibrated measurementsare able to closely agree with reference measurements froma high-end device. Sensor calibration is indispensable bothbefore and after the deployments of low-cost air pollutionsensors. Pre-deployment calibration is crucial to identify theprimary error sources, select and train calibration models forlow-cost sensors to properly function in the target deployment.Periodic post-deployment calibration is necessary to maintainconsistency among distributed sensors and ensure data qualityof long-term deployments.

Although calibration for air pollution sensors dates backto decades ago [15], [16], it has attracted increasing researchinterest because (i) newly available air pollution sensors pushthe boundaries in terms of power consumption and portabilitywhile neglecting sensing accuracy; and (ii) air pollution sen-sors are deployed in new scenarios such as in crowdsourcedurban sensing [17] and personal sensing [18], [19].

Related Surveys. Several surveys discuss low-cost air pollu-tion sensor solutions and their different applications in real-world deployments. Rai et al. [5] summarize existing low-

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cost air pollution sensor technologies and divide them intotwo groups, particulate matter (PM) and gaseous sensors. Thesurvey provides an overview of existing testing and evaluationreports that highlight various important characteristics andlimitations of state-of-the-art sensors. Similar articles focuson sensors for particular pollutants, e.g., Spinelle et al. [7]on volatile organic compounds (VOC) and benzene mea-surements, Jovasevic et al. [6] on particulate matter andBaron et al. [8] on electrochemical sensors for gaseous pollu-tants. Yi et al. [9] review the existing applications of low-costair pollution sensors in static, vehicle and community basedsensor networks. Thompson [17] provides an in-depth reviewof crowdsourced air pollution monitoring and their currentdemands and requirements for future successful deployments.

Our Contribution. While the related survey articles highlightthe generally low accuracy of low-cost sensors, there is a lackof a comprehensive review of the reasons for the low dataquality and calibration methods to improve it. In this articlewe summarize the existing scientific literature and give an in-depth list of different limitations of state-of-the-art low-costsensors. The majority of this survey is devoted to differentcalibration models that have been proven successful in tacklingthe limitations and improving the data quality of low-cost airpollution sensors, and effective methods to re-calibrate large-scale air pollution monitoring deployments. The discussedworks stem from different research communities includingatmospheric chemistry, measurement technology and sensornetworks. Thus, this survey provides a global picture of thediverse scientific results.

Roadmap. In Sec. II we describe the most prominent sensingprinciples used in low-cost sensors. Further, we describe 6common limitations that lead to generally inaccurate mea-surements. In Sec. III we present three calibration modelsthat are used to counteract different limitations that pose achallenge in any sensor deployment. In Sec. IV we specificallyfocus on methods that maintain high data quality in long-term deployments. These network calibration methods aretailored to re-calibrate the models presented in Sec. III in real-world deployments where access to highly accurate referencemeasurements is scarce. Finally we conclude this survey inSec. V and discuss multiple possible future work directions.

II. AIR POLLUTION SENSORS

Fast advances in technology and strong commercializationefforts are main drivers for an increasing number of low-cost sensors available nowadays [20]. Compared to high-end monitoring systems low-cost sensors typically requiresignificantly less power and smaller packaging. Although theseproperties make low-cost sensors favorable for various large-scale monitoring applications, a diverse list of limitationshinders them to achieve a similar level of data quality as moresophisticated sensors. This section reviews the sensing tech-nologies of low-cost air pollution sensors, summarizes theirmost common error sources, and points out the calibrationopportunities to improve their measurement accuracy.

A. Sensor Types and Sensing Principles

As highlighted in [5], [9], common low-cost sensors canroughly be divided in two groups defined by their target pollu-tant, i.e., particulate matter (Sec. II-A1) and gases (Sec. II-A2).

1) Particulate Matter Sensors: Particulate matter (PM)describes a mixture of solid and fluid particles, which are typ-ically classified by their size in diameter. PM10 describes themass concentration of particles with a diameter smaller than10µm, PM2.5 smaller than 2.5µm. Ultrafine particles (UFP)are nano-particles with diameters usually below 0.1µm. Theseparticles are known to cause serious effects on environmentand human health and, thus, monitoring their concentration,size distribution and composition is of high importance [2].

Low-cost PM sensors are almost exclusively based on op-tical sensing principles. The most prominent principle is basedon light scattering, where air is pumped into a small chamber.Inside the chamber a light source, either an LED or a low-power laser, is illuminating the air. Depending on the numberof particles in the air mixture, the light is scattered withdifferent intensity, which can be measured by a photodiode.Certain low-cost PM sensors apply more sophisticated opticalprinciples to also differentiate sizes of particles.

2) Gas Sensors: The most relevant gaseous pollutants inoutdoor air with serious negative effects on human beings,animals and the environment are sulphur dioxide (SO2), oxidesof nitrogen (NO, NO2, NOx = NO + NO2), carbon monoxide(CO) and ozone (O3) [2]. In indoor air mainly carbon dioxide(CO2), volatile organic compounds (VOC) and in some casesalso carbon monoxide (CO) are known to be possibly presentin harmful concentrations [21].

The majority of commercially available low-cost gas sensorsis therefore targeting to measure the concentration of one ofthese gases. With the exception of CO2, which is either directlymeasured with light scattering sensors [20] or approximated bythe presence of VOCs [22], the most popular sensing principlesare based on electrochemical or metal oxide layer reactions.• Electrochemical. An electrochemical sensor (EC) consists

in its simplest form of two electrodes, a working electrodeand a counter electrode. Gases are either oxidized or re-duced at the working electrode, which results in electroniccharges generated. The generated potential difference atthe two electrodes allows a current flow. This currentis usually linearly proportional to the gas concentration.More advanced electrochemical sensors incorporate oneor two additional electrodes to improve stability andsensitivity [23], [24].

• Metal oxide. Metal oxide sensors (MOX) use a sensinglayer, where gases are either absorbed or desorbed. Thisreaction causes a change in conductivity of the material.In order to increase sensitivity the sensing layer needs tobe heated to temperatures of at least 250◦C. State-of-the-art metal oxide sensors are capable of measuring all themajor gaseous pollutants [25].

Based on the above sensing principles, manufacturers pro-duce low-cost sensors and offer different features. Somesensors solely output an analog signal while others offer on-device signal processing, e.g., digitization of the analog signals

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Fig. 1. Overview of typical low-cost error sources and their correspondingcalibration approaches indicated by gray lines.

or internal calibration. In the remainder of this survey we donot differentiate between these different features. We regarda low-cost air pollution sensor as a black box with a signaloutput. The sensor is applied out-of-the-box and its outputis used for comparison and calibration with references. Thisis the general approach done in the studies presented in thissurvey.

B. Error Sources

One of the most essential questions regarding the aforemen-tioned low-cost sensors is how their measurements performin comparison to high-quality references. An ideal sensorfully agrees with its corresponding reference sensor, i.e.,exhibits a perfect linear relationship, as illustrated in Fig. 2a.Unfortunately, the main reason why low-cost sensors have notyet been established as a trust-worthy air pollution monitoringfashion is their generally poor measurement accuracy [11]–[14]. In an exhaustive test report by Jiao et al. [12] performa black box testing approach for multiple sensors. Out of 38tested sensors only 17 correlate well to their correspondingreference sensors. Through exhaustive sensor testing schemesand signal analysis researchers were able to detect multipledifferent error sources of state-of-the-art low-cost sensors. Asa result, most low-cost sensors significantly deviate from anideal sensor (Fig. 2).

We divide the error sources in two groups, internal andexternal error sources, also summarized in Fig. 1. Note that wedo not include error sources that have not yet been thoroughlytackled by calibration methods, such as slow response time orsensor mobility effects [26], [27].

1) Internal Error Sources: Internal error sources are gener-ally known error sources and typically related to the workingprinciple of low-cost sensors.

• Dynamic Boundaries. Dynamic boundaries define therange of a pollutant concentration in which a sensor issensitive to. Especially the lower boundary, the limit ofdetection (LOD) [28], is important. Below this boundarythe noise of a sensor signal starts to dominate and it be-comes impossible to differentiate between concentrationlevels. Low-cost sensors often have a LOD that is closeto the range of interest or even surpasses it. As a result,measurements at low pollution concentration are subjectto high noise. An example of a low-cost sensor affectedby high noise at low concentration due to imperfectdynamic boundaries is depicted in Fig. 2b. EspeciallyPM [5] and electrochemical sensors [29] are known to besignificantly affected by low signal-to-noise ratios at lowconcentrations. It is important that calibration proceduresare applied with respect to this limitations.

• Systematic Errors. Systematic errors are of non-randomnature and typically either characterized by a constantoffset over the whole range of concentrations or anunder- or overestimation of the concentration in certainranges [11], [13], [14]. An example of a sensor responsewith a constant offset is illustrated in Fig. 2c. They canoften be attributed to imperfect calibration parameters andare generally not related to the sensing principle. Popularexamples where systematic errors pose a challenge arefactory calibrated sensors, as elaborated in detail inSec. III.

• Non-Linear Response. Due to the nature of certain low-cost sensing techniques non-linear relationships betweena sensors and a references response are unavoidable. Non-linear behavior is known to be an issue particularly for awide range of particulate matter sensors [30], [31] andmetal oxide sensors [32]. Often sensor manufacturersalready linearize the sensor response, e.g., by internalsignal processing, or provide information about typicalnon-linear behavior in the datasheet. However, additionalfactors such as environmental conditions are known tocause non-linear behavior as well [33]. Fig. 2d showsan example of a non-linear sensor response. A linearrelationship is in general favorable because it allows theuse of simple calibration models.

• Signal Drift. Low-cost sensors generally cannot maintaina stable measurement performance over a long time [34]–[36]. This usually happens due to aging and impurityeffects, and leads to a slow drift of the sensors sensitivity.Signal drift is one of the most common error sources andseriously impedes long-term deployments with low-costsensors.

2) External Error Sources: External error sources are in-duced by the working conditions of a sensor, such as en-vironmental factors, and therefore are heavily deploymentdependent.

• Environmental Dependencies. Changing environmentalconditions can cause problems that almost any low-costsensor is facing. Various laboratory reports show that cer-tain physical ambient properties, especially temperatureand humidity conditions, can have a serious effect on

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Fig. 2. Comparison of measurements (arbitrary unit) from a reference sensor (x-axis) versus measurements of different low-cost sensors (y-axis). Fig. 2aillustrates the response of a perfect low-cost sensor, Fig. 2b of a low-cost sensor affected by high noise at low concentration due to imperfect dynamicboundaries, Fig. 2c of a low-cost sensor suffering from systematically overestimated measurements and Fig. 2d of a senor with a non-linear response. Theideal response is a perfectly linear relationship between low-cost sensor and reference.

a sensors response. For instance, increasing humidity isnotably decreasing the sensitivity of metal oxide [24],electrochemical [37] and particulate matter sensors [38].As a result, low-cost sensors usually perform significantlyworse in field deployments than in a laboratory setup.Further, environmental dependencies can also be respon-sible for non-linear responses, e.g., for electrochemicalsensors [33].

• Low Selectivity. Typical metal oxide and electrochemicalsensors suffer from low selectivity. This means they arenot exclusively sensitive to their intended target gas butare also cross-sensitive to, sometimes various, interferingsubstances in the air [39]. Especially in complex outdoorair these cross-sensitivities impose a fundamental chal-lenge for low-cost gas sensors. Particulate matter sensorsare usually not affected by cross-sensitivities because theyare intended to detect a composition of different parti-cles. However, in some cases where low-cost particulatematter sensors are either used to detect particles fromcertain sources like car exhaust or to distinguish differentparticle sizes, cross-sensitivities are also considered as afundamental error source [5]. Compared to environmentaldependencies, the low selectivity problem is caused bypurely chemical inferences and requires more sophisti-cated calibration efforts.

C. Sensor Deployments and Calibration Opportunities

A commonly used solution to reduce the errors of low-cost air pollution sensors is calibration. Calibration finds arelationship i.e., a calibration model that maps the measure-ments of a low-cost sensor to those of an accurate referencesensor. Sensor calibration is performed both before and afterthe deployment of air pollution sensors to deal with differenterror sources (see Fig. 1).

1) Pre-deployment Calibration: The aim of pre-deploymentcalibration is to try to identify all possible internal and externalerror sources of a sensor in an observed and/or controlledenvironment before deploying the sensor in the field. Pre-deployment calibration usually assumes continuous availabil-ity of a high-quality reference sensor. One or multiple errorsources listed in Fig. 1 can be detected by comparing thelow-cost sensor to the reference sensor. These error sourcesare then tackled by developing a suited calibration model(Sec. III).

2) Post-deployment Calibration: Post-deployment calibra-tion is used for counteracting error sources that impede aconsistent performance of a calibration model over time or inthe actual deployment environment. These error sources areeither heavily deployment dependent, such as harsh environ-mental conditions, or due to signal drift, which commonlyoccurs in long-term deployments. During post-deploymentcalibration, large numbers of sensors with irregular accessto reference measurements need to be calibrated. This isachieved by applying the calibration models extracted frompre-deployment calibration to different network re-calibrationstrategies (Sec. IV).

In Sec. III and Sec. IV we outline the existing calibrationapproaches, which are found in literature and used in low-costair pollution sensor deployments.

III. CALIBRATION MODELS

Calibration models are applied in both pre-deploymentand post-deployment calibration. We start with the basicand fundamental model, i.e., offset and gain calibration, inSec. III-A. Building on this basic model Sec. III-B presentsa first extension that corrects for temperature and humidityeffects. Finally Sec. III-C summarizes an additional extensionof the previous two models by also considering potentialinterference from other pollutants.

A calibration model takes the raw measurements of a low-cost sensor and transforms them to calibrated measurements,leveraging prior knowledge e.g., datasheets or additional in-formation e.g., measurements from auxiliary sensors. Variousmathematical methods can be applied and calibration modelsmay vary for different types of sensors. Calibration parameterscan be derived through measurements either in a laboratorysetup (controlled environment) or in the field next to referencemonitoring sites (observed environment). Table I provides asummary of available literature and different characteristicswith respect to the three calibration models. We exclusivelyfocus on calibration models that are either specifically tailoredfor air pollution sensors or general models that have beenproven successful when applied to real-world air qualitysensors.

A. Offset and Gain Calibration

Offset and gain calibration tackles calibration errors dueto dynamic boundaries and systematic errors and removes

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TABLE IOVERVIEW OF SENSOR CALIBRATION MODELS PRESENTED IN LITERATURE.

Calibration Model Author Method Setup Sensors

Offset and Gain Calibration

Castell et al. [11] Ordinary Least Squares Lab & Field ECSpinelle et al. [13], [14] Ordinary Least Squares Field EC, MOX

Austin et al. [31] Exponential Curve Fitting Lab LSCheng et al. [40] 2nd Order Curve Fitting Lab LSCarotta et al. [41] Linear & Non-Linear Curve Fitting Field MOXDacunto et al. [30] Power Law Curve Fitting Field LSBalabin et al. [42] Support Vector Regression Lab LS

Temperature and Humidity Correction

Holstius et al. [43] Multiple Least Squares Field LSPiedrahita et al. [20] Multiple Least Squares Lab & Field MOX, LS

Jiao et al. [12] Multiple Least Squares Field EC, MOX, LSSun et al. [44] Multiple Least Squares Lab & Field EC

Martin et al. [45] Multiple Least Squares Lab LSEugster and Kling [46] Multiple Least Squares Field MOX

Barcelo-Ordinas et al. [47] Multiple Least Squares Field MOXHagan et al. [29] Multiple Least Squares, kNN Field EC

Wei et al. [48] Linear & Non-Linear Curve Fitting Lab & Field ECPopoola et al. [33] Linear & Exponential Curve Fitting Lab & Field EC

Mead et al. [23] Linear & Non-Linear Curve Fitting Lab & Field ECGao et al. [49] Higher Order Polynomial Fitting Field LS

Masson et al. [32] Non-Linear Curve Fitting Lab & Field MOXTsujita et al. [50] Non-Linear Curve Fitting Lab & Field MOXSohn et al. [51] Exponential Curve Fitting Lab MOX

Sensor Array Calibration

Pang et al. [37] Multiple Least Squares Lab & Field ECSpinelle et al. [13], [14] Multiple Least Squares Field EC, MOX

Maag et al. [52] Multiple Least Squares Field EC, MOXFang et al. [53] Multiple Least Squares Field MOX, LSCross et al. [54] Non-Linear Curve Fitting Field EC

Zimmermann et al. [55] Random Forests Field EC, LSKamionka et al. [56] Neural Networks Lab MOX

Spinelle et al. [13], [14] Neural Networks Field EC, MOXBarakeh et al. [57] Neural Networks Field MOX

De Vito et al. [58], [59] Neural Networks Field MOXEsposito et al. [60], [61] Neural Networks Field EC

Esposito et al. [62] Various machine learning methods Field ECDe Vito et al. [63] Various machine learning methods Field ECLewis et al. [64] Various machine learning methods Lab & Field EC, LS

Note: EC: Electrochemical, MOX: Metaloxide, LS: Light-Scattering (Particulate Matter and CO2)

potential non-linear responses. It is one of the most essentialcalibration models that maps the raw sensing measurementsto a target pollutant concentration.

1) Principles: Offset and gain calibration fits a calibrationcurve, either a linear or a non-linear one, to model relation-ships between raw sensor readings and pollutant concentra-tions. The calibration curve is defined by an offset term,i.e., the sensor’s response to complete absence of the targetpollutant, and a gain term that characterizes the sensor’sresponse to increasing pollutant concentrations. Optimal offsetand gain parameters capture the behavior of a sensor withinits sensitivity range, i.e., the dynamic boundaries, and removesystematic errors attributed to poorly fitted calibration param-eters.

2) Methods: The most popular methods to calculate offsetand gain terms are ordinary least squares for a linear cali-bration line and non-linear curve fitting, for instance with anexponential [31] or power law [30] gain term. Offset and gaincalibration can be performed in both lab and field setups.• Lab Tests. One way to acquire a calibration curve is to

expose a sensor to various target pollutant concentrationsin a controlled laboratory setup. Austin et al. [31] exposea low-cost PM sensor to different aerosol air mixturesin an air-tight enclosure. The gathered measurements areused to calculate a calibration curve defined by an offset

Fig. 3. Governmental monitoring station located in a suburban area inSwitzerland.

and an exponential gain term. Castell et al. [11] follow asimilar approach and calibrate different electrochemicalsensors by exposing them to five different gas mixingratios. Their sensors show high correlation (R2 ≥ 0.92)and, thus, a simple linear calibration based on ordinaryleast squares was used to adapt the offset and gain terms.Similar laboratory calibration can be found in additionalworks [40], [42]. For certain commercially available low-

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cost sensors an initial laboratory calibration is alreadyperformed in the factory. Manufacturers usually followsimilar approaches as found in the literature and eitherprovide the sensors response over a range of target pol-lutant concentrations [65] or in the form of a calibrationcurve recorded in a laboratory setup [66].

• Field Tests. Various recent works propose to directlycalibrate their sensors in an environment that is similarto the final deployment. The most prominent way isinstalling the sensors under test next to high-end sensors.For instance, Dacunto et al. [30] jointly deploy a low-costPM2.5 sensor with a high-end device in different indoorlocations. In outdoor deployments the most prominentapproach is to install the sensors under test directly nextto governmental monitoring stations that often featurea variety of accurate pollution sensors. For instance,Fig. 3 shows a monitoring station of the governmental airquality monitoring network in Switzerland. Spinelle et al.[13], [14] deploy 17 different low-cost gas sensors next tohigh-quality sensors of a air quality monitoring station ina semi-rural area. Carotta et al. [41] deploy differentMOX sensors next to a monitoring station located ata high traffic road and next to one in a low trafficintensive area. The highly accurate measurements fromthese monitoring stations are used to train and evaluatethe calibration of the low-cost sensors.

3) Discussion: While laboratory setups are faster than fieldtests, many researchers [11], [20], [32], [41] recommend fieldtests for offset and gain calibration. In a laboratory setup,the environmental conditions during exposure are typicallyheld constant, e.g., at room temperature and moderate relativehumidity. Further, the chamber is usually filled with cleanair mixed with the target pollutant concentration, i.e., withoutpossible interference from other pollutants. In contrast, fieldtests allow that the sensors to be exposed to situations withrealistic environmental conditions, e.g., changing meteorolo-gical parameters or interfering gases. Because the sensors areexposed to realistic pollution concentrations the parameterscan be optimized to capture the behavior of the sensor withinexpected concentration ranges, i.e., with respect to the dynamicboundaries. For instance, Castell et al. [11] calculate anoffset of their calibration curve around 1 ppb in a laboratorycalibration and around 166 ppb in a field calibration for a COsensor. By re-calibrating the CO sensor, i.e., adapting its offsetterm, in the field they finally reduce the measurement errorfrom 181 ppb by over a factor 2 to 87 ppb. Zimmermann et al.[55] show similar results with four different sensors. Offsetand gain calibration models calculated in a laboratory performpoorly in an outdoor deployment and are not in line with re-calibrated models.

As explained in Sec. II-A2, errors of air pollution sensorscan be environment-dependent. In part, in-field offset and gaincalibration implicitly mitigates the impact of these externalerrors. However, environmental conditions are complex andsubject to short- and long-term changes. As a result, simpleoffset and gain calibration achieves significantly worse resultsin field than in laboratory tests. For instance, Castell et al. [11]

observe a drop of R2 = 0.99 to 0.3 of a NO2 sensor whenmoving from laboratory to field tests. To explicitly account forthese environmental conditions temperature, relative humidityand interfering gases, advanced calibration models are needed,as we will describe in Sec. III-B and Sec. III-C.

B. Temperature and Humidity Correction

Temperature and humidity correction augments air pollutionmeasurements with concurrently measured temperature andhumidity readings to calibrate the low-cost air pollution sensor.

1) Principles: The motivation of temperature and humiditycorrection stems from the influence of different temperature orrelative humidity settings on sensors observed in laboratorytests. Pang et al. [37] observe a relative drop in sensitivityof roughly 20% for electrochemical sensors when the relativehumidity is increased from 15% to 85%. A similar observationis made by Wang et al. [24] for a metal oxide sensor. Thesensor almost completely loses its sensitivity when chang-ing from dry air to an extreme relative humidity of 95%.Wang et al. [38] demonstrate that increasing humidity canlead to an overestimation of the particle number of typicallow-cost light scattering sensors. Similar sensitivity lossesare also experienced under changing ambient temperature assummarized by Rai et al. [5]. These results make it evident thatchanging environmental conditions such as temperature andhumidity need to be incorporated in the calibration process inorder to improve the overall measurement accuracy of virtuallyany low-cost air pollution sensors.

2) Methods: Temperature and humidity correction is ubiq-uitous due to the availability of cheap and small but pre-cise low-cost temperature and humidity sensors. Most worksinclude these additional measurements in their calibrationmethods, and extend the single-variant mathematical modelsin offset and gain calibration (Sec. III-A) to the correspondingmulti-variant models.

A simple approach found in most of the investigation is tofind the linear combination of raw air pollution, temperatureand humidity sensor measurement that best captures the targetreference concentration. The results in [12], [20], [29], [43]–[46] all use multiple least squares to calculate this combinationand show beneficial results for any type of low-cost sensor.Different approaches apply more complex methods to modelthe impact of temperature and humidity. Masson et al. [32]derive a detailed model that captures the physical effect ofambient temperature on their MOX sensor. Popoola et al.[33] develop a temperature baseline correction algorithm forelectrochemical sensors. They observe notable differences intemperature sensitivity for carbon monoxide (CO) and nitrogenoxide (NO) sensors. While the CO sensor showed a linearrelationship to its reference, the NO sensor exhibits a strongexponential relationship. Therefore they model the reactionto temperature with a linear line fit for the CO sensor anda exponential curve fit for the NO sensor, which is used tocorrect the corresponding sensor signal. They are able to showa significant improvement for the NO sensor by improving thecorrelation from R2 = 0.02 to R2 = 0.78. Tsujita et al. [50]and Sohn et al. [51] similarly model the relationship of MOX

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sensors to humidity and temperature with exponential termsand compensate for them by fitting a calibration curve.

3) Discussion: The extensive list of different sensors thatsignificantly improve their accuracy after temperature andhumidity correction underline the severity of the problem.Temperature and humidity correction needs to be performedfor any air pollution sensor regardless of its underlying sensingprinciples. In rare cases, the impact of ambient conditionscan be precisely modeled using chemical process theory. Thisapproach however requires deep knowledge of the underlyingsensing principle, e.g., physical properties of the metal oxidesensing layer. Therefore, more simpler data driven methodsdominate the different calibration methods. Due to the popular-ity of the problem recent low-cost sensors, especially fully dig-ital sensor solutions, already integrate an internal temperatureand humidity correction [66], [67]. However, the various fieldcalibration works emphasize the benefit of directly compensatefor temperature and humidity dependencies. Thus, it becomesevident that static correction schemes by manufacturers orlaboratory calibration may be replaced by in-field calibrationfor optimal performance.

C. Sensor Array Calibration

Sensor array calibration is a generic extension of tempera-ture and humidity correction that tackles another environmen-tal dependent factor, interfering gases.

1) Principles: As described in Sec. III-A laboratory testsare usually performed by exposing the sensor to clean airthat is mixed with the target pollutant. In most real-worlddeployments the air mixture is composed of multiple differ-ent components [23]. For instance, in outdoor and commonindoor air multiple pollutants appear concurrently at diverseconcentrations. These complex air mixtures particularly posea substantial challenge for gaseous pollutant sensors. Insteadof being selective to one single pollutant, low-cost sensorsare typically sensitive to multiple pollutants at the sametime with different intensities [24], [39]. This low-selectivityproblem is also referred to as cross-sensitivities and, broadlyput, equivalent to the temperature and humidity dependency,i.e., different factors in the environment are influencing asensors response. Thus, the basic concept is the same as thetemperature and humidity correction but often requires morecomplex methods.

By concurrently measuring all the cross-sensitivities it ispossible to compensate for all interfering pollutants. Thisapproach requires a sensor array, i.e., multiple different jointlydeployed low-cost sensors. One option to create a sensor arrayis to install multiple sensors in a box to ensure commonair sampling. Note that the majority of sensor arrays alsoinclude temperature and humidity sensors and, thus, in thiscase sensor array calibration is also performing a temperatureand humidity correction.

2) Methods: Popular sensor array calibration methods canbe divided in multiple least squares and neural networks.• Multiple Least Squares. For certain cross-sensitivity

problems a multiple least squares regression can besuccessfully used for calibration. One of the most popular

examples is the cross-sensitivity of NOx EC sensors onO3 concentrations [52], and vice-versa [37]. Pang et al.[37] are compensating for potential influences of ambientNO and NO2 concentrations on the signal of a O3 ECsensor. The NO and NO2 concentrations are howevermeasured by a high-end sensing device. The effect of thetwo cross-sensitivities follow a linear behavior and, thus,a linear multiple least squares calibration can be success-fully applied. Another investigation [52] follows a similarapproach, but compensates for the cross-sensitivity toO3 of a NO2 EC sensor. The O3 measurements aremeasured by another low-cost metal oxide sensor. It isshown that the measurement error of the cross-sensitiveNO2 sensor can be reduced by over 80% by simplyincorporating measurements of an additional O3 sensorin the calibration. Multiple least squares are effective tocompensate for cross-sensitivities of (i) electrochemicalsensors to (ii) the oxidizing gases NOx and O2.

• Neural Networks. In more complex cases, linear cali-bration models do generally not perform well [13], [14]and, therefore, different authors investigate the feasibilityof non-linear calibration models, mostly based on neuralnetworks or related machine learning methods, see Ta-ble I. Spinelle et al. [13], [14] show for a wide rangeof low-cost gas sensors an overall better performance ofneural network based sensor array calibration comparedto multiple least squares and particularly to a offset andgain calibration based on ordinary least squares. For mul-tiple O3 and NO2 sensors the coefficient of determinationR2 is improved from values below 0.3 to at least 0.85 and0.55 respectively using neural networks instead of linearmodels. They also show that for some sensors, in par-ticular metal oxide CO and electrochemical NO sensors,the cross-sensitivity limitation appears to be too severeand could not be solved by calibration with reasonableperformance. Similar results are reported by De Vito et al.[58], [59], [63], Esposito et al. [60]–[62], Lewis et al.[64], Barakeh et al. [57] and Zimmermannet al. [55].Different types of machine learning techniques, with themajority being neural networks, are able to resolve cross-sensitivities of commercial low-cost sensors with the helpof sensor array calibration.

3) Discussion: Compared to the other two calibration mod-els, sensor array calibration is not a necessity for all sensors.The necessity of sensor array calibration mainly depends onthe sensitivity profiles of low-cost sensors and the target pol-lutant. For instance, O3 can in general be accurately measuredwith a single low-cost sensor due to the aggressive nature ofozone that in return simplifies the development of selectivesensing principles. Other pollutants, for instance NOx, areaffected by the presence of aggressive interference factors andcomplicate the design of selective sensors. This two interactingfactors pose a substantial challenge in choosing the optimalsensor array composition, i.e., what low-cost sensors arerequired to accurately measure the target pollutant. Therefore,various works [54], [55], [59] present a thorough analysis onwhich sensor array composition achieves the best performance

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in terms of measurement accuracy, precision and stability.Such an analysis requires concurrent data of multiple differentlow-cost sensors that need to be tested on their feasibilityin different sensor arrays. In some cases, the available low-cost sensors may not suffice for a successful array due tounresolved cross-sensitivities [13]. Thus, finding the optimalsensor array to tackle all cross-sensitivities remains an openproblem. Further, similar to the two previous models authorsagree that pre-deployment sensor array calibration needs to beperformed in the field. The complex composition of pollutantsin outdoor air requires the sensors under test to be exposed intheir target deployment for a successful calibration.

D. Comparisons of Calibration Models

In summary, the most essential calibration model that isnecessary for all types of sensors is a simple offset and gaincalibration, i.e., mapping the raw sensor measurements to apollutant concentration. Popular mathematical methods arelinear regression or simple curve fitting possibly incorporatinga non-linear gain term. Due to the severity of the environ-mental dependency problem extending the basic model witha temperature and humidity correction becomes indispensablein order to significantly improve the measurement accuracyof any low-cost sensor. The correction can easily be done byconcurrently measuring environmental parameters and includethem in multi-variable methods, such as multiple least squaresor non-linear curve fitting. Finally, additional environmentalinfluences from interfering gases can be eliminated by incorpo-rating sensor array calibration techniques. Cross-sensitivitiesare mostly problematic for electrochemical and metal oxidesensors and heavily deployment dependent. Sensor array cali-bration requires concurrent measurements from different low-cost sensors and often sophisticated machine learning methodsto capture the complex relationship between multiple cross-sensitive sensor and the target pollutant concentration. Overallsensor array calibration has been shown to produce most accu-rate data. Spinelle et al. [13], [14] evaluate the performance ofthe three different calibration steps with different gas sensors.For instance, the NO concentration measured by a calibratedsensor array achieves 15 and 41 times lower measurementerrors compared to a single NO sensor with and withouttemperature correction respectively. Similar results are shownby Zimmermann et al. [55]. Their sensor array calibrationbased on both linear and non-linear methods achieves analmost one order of magnitude lower error than a simplelaboratory offset and gain calibration for four different typesof sensors.

The number of additional sensors and the amount of mea-surements needed to learn the model parameters increase withthe complexity of calibration models. Compared to the othertwo calibration models, sensor array calibration also requiresmore training samples, i.e., covering a large range of differentoutdoor situations and, thus, is more time-consuming andcomplex to perform. De Vito et al. [58] show a clear positivetrend of accuracy and precision with increasing training data.Finally they achieve a stable calibration with training datacollected over 100 days. These long training epochs efforts are

however justified in order to achieve high data accuracy duringlong-term deployments possibly spanning multiple years.

Note that a prerequisite to apply calibration models is theaccess to a highly accurate reference. A reference is usuallyavailable in lab or field tests before actual deployment of airpollution sensors. However, the sensors after deployment mayhave irregular access to a reference, which requires additionalcalibration strategies, as we will discuss in the next section.

IV. NETWORK CALIBRATION

Low-cost sensors are usually deployed in either a static ormobile sensor network for long-term air pollution monitoring.Even after pre-deployment calibration, these sensors need peri-odic re-calibration due to sensor drift over time and changes inthe target environments. Some works report a significant driftafter already 1 month of deployment [35]. Thus, re-calibratingsensors appears to be an absolute necessity in any long-termdeployment.

An important commonality of post-deployment calibrationis the lack of reference sensors to verify and potentiallyre-calibrate low-cost sensors. This section reviews existingnetwork re-calibration methods, which calibrate a network ofsensors with irregular or even no access to a highly accuratereference. We group the existing literature into three funda-mental network calibration approaches, i.e., blind (Sec. IV-A),collaborative (Sec. IV-B) and transfer (Sec. IV-C) calibration,based on their assumptions or usage of virtual references.Table II holds a list of works that present network calibrationmethods specifically tailored for air quality sensors. Notethat calibration in sensor networks is a general problem and,thus, some of the presented methods can also be directlyapplied or adapted to other type of sensor network applicationsconsisting of temperature and relative humidity sensors [91],microphones [92] or barometers [93].

A. Blind Calibration

The concept of blind calibration [94] or macro calibration,is originally designed for general sensor networks and hasalso been applied to temperature and relative humidity sensornetworks [91], [94]. The idea is to achieve a high similar-ity between measurements of all sensors in a network. Akey assumption is that neighboring sensors measure almostidentical values, or are at least correlated. This assumptionis often not true for air pollution monitoring deployments.First, air pollution is known to be a highly complex systemwith large spatiotemporal gradients. Second, typical inter-device differences of low-cost air pollution sensors hinderequal measurements even in a dense small-scale network. Asa result measurements of air pollution sensors in a large-scaledeployment are in general neither identical nor necessarilycorrelated. A more practical assumption is to exploit situationsin space and time where we can safely assume that all sensorswithin the given deployment measure the same pollutionconcentrations.

Tsujita et al. [50] installed a low-cost NO2 sensor in the cityof Tokyo, Japan. They recognize that the major error sourceof their sensor appears to be baseline drift of the calibration

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TABLE IIOVERVIEW OF NETWORK CALIBRATION METHODS

Approach Author Linearity Mobility

Blind Calibration

Jiao et al. [12] Linear StaticFishbain et al. [68] Linear Static

Moltchanov et al. [69] Linear StaticBroday et al. [70] Linear StaticMueller et al. [35] Linear Static

Pieri et al. [71] Linear StaticTsujita et al. [50] Linear Static

Mix: Blind & Collaborative Calibration Dorffer et al. [72]–[74] Linear & Non-Linear Mobile

Collaborative Calibration

Xiang et al. [75] Linear MobileHasenfratz et al. [76] Linear Mobile

Saukh et al. [77] Linear MobileSaukh et al. [78] Linear MobileMaag et al. [79] Linear MobileBudde et al. [80] Linear Mobile

Fu et al. [81] Linear MobileMarkert et al. [82] Linear Mobile

Kizel et al. [34] Linear MobileArfire et al. [83] Non-Linear Mobile

Transfer Calibration

Cheng et al. [40] Non-Linear StaticZhang et al. [84] Non-Linear not relevantZhang et al. [85] Mix not relevant

Deshmukh et al. [86] Mix not relevantFonollosa et al. [87] Mix not relevantYan et al. [88], [89] Linear not relevant

Bruins et al. [90] MOX Heating not relevant

S1 S2

S3S4

R1

R2

Fig. 4. Blind calibration scenario with rurally located sensors S1, S2, ruralreference R1, urban sensors S3, S4 and urban reference R2. Sensors that arelocated in similar areas (rural or urban) are calibrated to references in similarareas during times when it is safe to assume that all sensor measurements areidentical.

parameters over time. Because they continuously install theirsensor at different locations where no accurate governmentalstations are deployed, they propose an auto-calibration method.The sensor can be calibrated to reference stations that are notnecessarily in their spatial vicinity when one can safely assumethat the NO2 concentration is almost identical at any point inthe deployment region. To check these circumstances they useNO2 measurements from four different monitoring stations andre-calibrate the offset term of their low-cost sensor as soon asall four stations report a NO2 concentration below 10 ppb. Asimilar method is also applied by Pieri et al. [71]. A slightlyadapted approach is presented by Moltchanov et al. [69].Instead of assessing the possibility of a uniform concentrationwith reference measurements, they use specific time periods.

In order to calibrate low-cost O3 sensors they assume thatthe O3 concentration is uniform during night time (01:00-04:00 AM), when local emissions of precursors, e.g., NO2

traffic emissions, are negligible. During these time periods theycalibrate six O3 sensors to the reference measurements of onemonitoring station. Because O3 usually reaches concentrationsclose to zero during night, this approach again only allowsfor an offset re-calibration. Finally, Mueller et al. [35] alsodivide their low-cost sensors in two groups, i.e., sensors thatmeasures traffic related pollution variations deployed in innercity areas and background pollution sensors in outer city areas.This scenario is also illustrated in Fig. 4. They assume thatat inner city locations O3 and NO2 concentrations are usuallyuniform during night and at outer city locations during theafternoon. Individual sensors installed in the inner city arethen calibrated to a remote monitoring station in the innercity during nighttime and correspondingly for sensors locatedin the outer parts of the city in the afternoon.

B. Collaborative CalibrationCollaborative calibration extends blind calibration by creat-

ing virtual references where two mobile sensors meet in spaceand time such that they should measure the same physicalphenomena. The basic idea of collaborative calibration is toexploit situations where two or more mobile sensors meet inspace and time, i.e., referred to as sensor rendezvous. Thenotion of sensor rendezvous can also be found in other sensornetwork problems, such as energy efficient data collection [95]or sensor fault detection [77]. Further, collaborative calibrationexploiting sensor rendezvous is also used in other sensor net-works, e.g., crowdsensing applications using microphones [92]or barometers [93].

Sensor rendezvous can be utilized as references for cali-brating mobile air pollution sensors. Sensors in a rendezvous

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M1

M2

M3

R1M4

RVRV RV RV

Fig. 5. Collaborative multi-hop calibration scenario exploiting sensor ren-dezvous (RV) between static reference R1 and mobile sensors M{1,2,3,4}.Whenever sensor M1 is in the vicinity of the reference R1 the low-cost sensorcan be calibrated. In return, the freshly calibrated M1 is calibrating M2 duringredenzvous, and so forth.

are assumed to sense the same physical air and the rangeof a rendezvous can be empirically determined. For instance,Xiang et al. [75] define a distance of at most 2 m betweentwo sensors to constitute a rendezvous in an indoor airpollution monitoring deployment. Saukh et al. [78] showthat a distance of 50 m in urban outdoor deployments is areasonable upper limit. Whenever a mobile low-cost sensoris in a sensor rendezvous with a highly accurate sensor, e.g.,from a governmental monitoring site, the low-cost sensor canuse the reference measurement for calibration [78].

Arfire et al. [83] apply a non-linear temperature correctionfor mobile electrochemical sensors in a collaborative fashionwith a reference sensor. Hasenfratz et al. [76] present threedifferent calibration methods based on weighted least squaresthat also incorporate the age of measurement at the time ofthe calibration parameter calculations. The methods in [76] arealso applied by Budde et al. [80] to calibrate PM sensors ina participatory sensing scenario. These methods assume thata sensor is in rendezvous with one or more reference sensorsmultiple times under different conditions so that the sensor cancollect a calibration dataset with high variance for calibration.

Unfortunately, not all sensors necessarily are in rendezvouswith reference sensors frequently enough. As a consequence,some sensors in the network cannot be re-calibrated. There-fore, some works additionally exploit rendezvous betweena freshly calibrated and an uncalibrated low-cost sensor. Inthis case a sensor that has been freshly calibrated is usedto calibrate an uncalibrated one, e.g., a sensor that has norendezvous with references. In return, the second freshlycalibrated sensor can also be used to calibrate others, and soon. Calibration is therefore performed in a chain-like fashionand, thus, this concept is also known as multi-hop calibration.A typical multi-hop calibration chain is illustrated in Fig. 5.Although multi-hop calibration allows to calibrate more sen-sors compared to calibration exclusively with references, italso poses multiple challenges. The most severe challengeis error accumulation over multiple hops, first reported byHasenfratz et al. [76] and in detail evaluated by Saukh et al.[78] and Kizel et al. [34]. Due to the nature of least squaresbased calibration models at every hop of the calibration chaincalibration errors are accumulated. To counteract this erroraccumulation Saukh et al. [78] propose to use an alternativemethod, i.e., the geometric mean regression. It is not sufferingfrom error accumulation, theoretically and practically proven,

S1

S2

S3R1

S4

Transfer

Master

Fig. 6. Transfer calibration scenario between a reference sensor R1 andsensors S{1,2,3,4}. In a first step sensors S{2,3,4} are standardized to a mastersensor S1 in order to achieve high similarity of raw measurements. In a secondstep a calibration model acquired by the master S1 with reference R1 istransferred to all other sensors S{2,3,4}.

and is successfully used for offset and gain calibration of areal-world air pollution network. In [79] Maag et al. present amethod that is tailored for sensor array calibration while alsonot suffering from error accumulation. Additional challengesof multi-hop challenges are tackled in [81], [82]. Fu et al.[81] study the effect of reference sensor placement on theperformance of multi-hop calibration and present an algorithmto optimally design a practical deployment of static referenceand mobile low-cost sensors. A privacy preserving multi-hop calibration scheme for participatory and crowd sensingdeployments is introduced by Markert et al. [82].

C. Transfer Calibration

The third group of network calibration methods is knownas transfer calibration. It has its origins mainly in industrialdeployments using electronic noses (e-noses), i.e., metal oxidesensor arrays for hazardous odor detection. Although therelated work mainly focus on e-nose calibration, transfercalibration can be applied to any sensor model. E-noses aretypically calibrated by neural networks to detect multiple dif-ferent odors or gases with one calibration model. Training sucha neural network requires a lot of effort mainly due to trainingsample collection and model optimization. Metal oxide sensorarrays do typically not produce identical responses comparedto similar arrays, even coming from the same productionbatch [85], i.e., there are significant inter-device differencesfor e-noses. Therefore each e-nose needs to be calibrated inde-pendently and mass production becomes an almost impossibletask. Transfer calibration tackles this problem by applying atwo-step calibration process. Assuming multiple e-noses, onee-nose acts as a master sensor. In a first step, all non-mastere-noses standardize their raw sensor array signals individuallyto the raw ones of the master. This step is usually performedby linear regression methods, such as robust regression [86],ridge regression [89], direct standardization [87] or weightedleast squares [85], and counteracts the inter-device differences.In a second step, the master node calibrates its responseto the target gas or odor concentrations, e.g., by training aneural network calibration model [85], [86]. This model is nowtransferred to all non-master nodes, as illustrated in Fig. 6.

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TABLE IIIDIRECT COMPARISON OF THE THREE NETWORK CALIBRATION METHODS.

Method Advantages DisadvantagesBlind + Applicable to static and

mobile sensors+ Simple approach+ All sensors in the net-work can be calibrated

- Only offset calibrationpossible

Collaborative + All calibration modelspossible+ Sensor rendezvous as-sures high confidence inidentical measurements ofmultiple sensors+ Best suited for mobileair pollution monitoringdeployments

- Only applicable to mo-bile sensors- Number of sensors thatcan be calibrated dependson sensor mobility- Non-linear calibrationremains an open challengein multi-hop calibration

Transfer + Applicable to static andmobile sensors+ Non-linear calibrationmethods for all calibrationmodels possible+ All sensors in the net-work can be calibrated

- Limited performance- Only works with identi-cal sensors- Little experience in real-world deployments

Other popular methods used in the second step are supportvector machines regression [87], [89] or classification basedmethods to classify the presence of a certain gas using supportvector machines [87], [89] or logistic regression [89]. Someworks also combine the two steps using a global trainingframework, such as auto encoders by Zhang et al. [84] or amixture of multi-task and transfer learning by Yan et al. [88].Bruins et al. [90] show that the standardization in the firststep can also be performed by applying an elaborate heatingtemperature control of the MOX sensor array.

Since transfer learning only requires one complex calibra-tion process for the master sensor array, it is clearly ableto minimize calibration efforts in large-scale deployments.Unfortunately transfer learning approaches have mainly beenevaluated in lab setups and not yet intensively in real-worlddeployments. One of the only transfer calibration adaptationsusing a real-world large-scale PM sensor deployment is pre-sented by Cheng et al. [40]. In a first laboratory calibration stepthe PM sensors are standardized to a master sensor using sec-ond degree curve fitting. In the second step a neural networkis used to perform a temperature and humidity correction. Theneural network is constantly updated through out the deploy-ment. Overall they achieve an increase in approximately 8%measurement accuracy compared to uncalibrated situations.

D. Comparisons of Network Re-calibration Strategies

The three network calibration approaches all rely on dif-ferent assumptions and fundamental design choices and, thus,also have different advantages. Table III compares the threemethods and list their advantages and disadvantages. Theleast complex method based on blind calibration exploitstime periods and locations of reference and low-cost sensorsfor calibration to assure that all sensors generate identicalmeasurements. While this approach can be applied to any typeof sensor in any deployment, the opportunities for calibrationare generally sparse and, hence, only offset and gain calibra-tion can be successfully performed. In order to increase the

opportunities for calibration, collaborative calibration exploitsmeeting points or rendezvous between sensors. Consequently,collaborative calibration can only be applied to mobile sensordeployments. Depending on the mobility of the sensors itmight not possible to calibrate all sensors within the network,e.g., a sensor with no rendezvous can not be calibrated. Sofar it is unclear how collaborative calibration scales with thenetwork size. This is not a substantial problem for the othertwo methods.

Finally, transfer calibration uses a two-step approach byfirst standardizing all deployed sensors to a master sensor andthen transferring calibration parameters acquired by the masterto all sensors. Transfer calibration has no restrictions on thepossible calibration models or the mobility of sensor, withthe exception of the static master sensor next to a reference.However, transfer calibration assumes that all sensors in thenetwork (i) drift in a equal way as the master node and (ii)are equally affected by environmental conditions. These twoassumptions are in general not true in typical air quality moni-toring networks [85]. Therefore, up to now transfer calibrationhas not achieved satisfactory performance. Further, there isonly little experience in real-world deployments.

Overall, all the methods have been proven to be suc-cessful in counteracting decreasing accuracy in their specificlong-term deployments. In general the average measurementaccuracy is increased after re-calibrating a sensor networkand, thus, the existing results point out the necessity of re-calibration. However, the different strengths and weaknessesof the three methods presents the need for an universalnetwork calibration method. Currently, there is no one-for-allnetwork calibration solution available. Recent research effortsinvestigate the possibility of a general applicable network cali-bration method, e.g., by combining different aspects from thethree methods. Some theoretical investigations already providemixtures of different models. For instance, Dorffer et al. [72]–[74] combine the two ideas of blind and collaborative net-work calibration to increase the possibilities for sensor re-calibration. A key benefit of enhancing and mixing differentnetwork calibration aspects will thus help to assure that allsensors in a network can be calibrated. We discuss a detailedpossibility in Sec. V.

V. DISCUSSIONS AND CONCLUSIONS

In this survey, we review the sensing principles and errorsources of low-cost air pollution sensors, and the calibrationmodels and re-calibration strategies to improve the accuracyof these sensors before and after their deployments. Back todecades ago, air pollution information was accessible onlyat coarse spatiotemporal resolution. Advances in portableair pollution sensors have enabled fine-grained air pollutionmonitoring at low cost. Along with the convenience brought bylow-cost sensors come with the challenges in ensure quality oftheir measurements. We demonstrate the effective calibrationmodels and strategies suited to improve the accuracy of diverseair pollution sensors in various deployments. In the era ofInternet of Things, where air pollution monitoring becomesmore crowdsourced and personal, we also identify several

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largely open and attractive opportunities for future sensorcalibration research.

Calibration model benchmarking. Popular ways to assessthe performance of calibration models are metrics related tomeasurement error and correlation. A widely used metric is theroot-mean-squared-error between the calibrated measurementsand its reference counterpart. Equally popular is the coefficientof determination R2, which captures the amount of varianceof the reference measured is finally captured in the calibratedmeasurements. There exist a variety of other statistical mea-sures used in related work. An open challenge in assessing theperformance of calibration methods is a unified way to declarea limit of these metrics when the calibrated measurementsuffices for a certain application. Some researchers already fol-low benchmarks proposed by official authorities, for instancethe data quality objective (DQO) presented by the Europeanparliament [7], [11], [14]. The DQO provides a clear metricthat air quality sensors need to satisfy in order to be appliedas official measurement provider. As expected calibratinglow-cost sensors in order to fulfill these objectives is verychallenging, but also not necessarily needed for quantitativeapplications such as personal exposure assessment. A possiblefuture direction is to build a benchmarking framework thatdefines data quality guidelines for low-cost air quality sensornetworks with respect to different pollutants and applications.

Context-aware network re-calibration. As presented inSec. IV, all network re-calibration schemes need to identifysituations where it is safe to assume that multiple sensorsmeasure the same or similar phenomenon. The re-calibrationopportunities are either based on coarse assumptions (in blindand transfer calibration) or mobility (in collaborative cali-bration). With the rise of big data and urban computing therelationship between a sensors context, e.g., detailed land-usedata, and the expected pollution concentration can be preciselymodeled and is deeply understood. By classifying sensorlocations according to their land-use context, e.g., nearbytraffic, elevation or population density, a number of confidentand new re-calibration opportunities can be increased. Thesecontext-based virtual re-calibration opportunities will greatlyimprove the calibration ability of a sensor network and allowadditional calibration models as well as mathematical methods.

Calibration with little overhead. Machine learning methods,such as neural networks, have become popular tools for sensorcalibration in the last few years. Although they offer powerfulcapabilities of capturing complex and possibly non-linear rela-tionships between multiple sensors, they require large amountsof measurements to train an accurate calibration model viastandard supervised learning. This can be a burden for modelupdating in network re-calibration, especially for sensors thathave limited reference samples. In addition, the number ofsamples available for calibration may vary for different sensorsin a deployment. Consequently, the accuracy of calibrationmodels can also differ for different sensors due to imbalancedtraining data. Some recent study [19] has exploited techniquessuch as semi-supervised learning to reduce the amounts oftraining data for sensor array calibration. However, it remainsopen how to reduce the training overhead of network re-

calibration and achieve consistent calibration accuracy for allsensors in a networked deployment.Quantification of Trust. Due to limited access to refer-ence data during a sensor network deployment not only re-calibration is a challenging task but also the evaluation ofthe calibration performance. Control mechanisms to assess thetrust of the calibrated measurements offer therefore additionalfuture research directions. Metrics such as accuracy boundsfor sensor measurements [96], discrete reputation scores [97]or inter-node sensor confidence [98] and correlation [77] canbe applied in a network-wide trust model to provide a notionof quality of service of the air quality monitoring sensornetwork. Additionally, by observing a trust metric one canestimate the need for re-calibrating certain sensors withinthe network or apply filtering methods to assure high dataquality. Different related works [99] propose trust mechanismsin general networks, however, these have not yet been appliedin the specific scenarios of air pollution monitoring networks.

ACKNOWLEDGMENT

This work was funded by the Swiss National ScienceFoundation (SNSF) under the FLAG-ERA CONVERGENCEproject.

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Balz Maag received his M.Sc. degree in electrical engineering and informa-tion technology from ETH Zurich in 2014. He is currently a Ph.D. student inthe Computer Engineering and Networks Laboratory (TIK) at ETH Zurich.His research interests include the development and optimization of algorithmsfor wireless sensor networks and crowd-sensing applications.

Zimu Zhou is currently a post-doctoral researcher at the Computer Engineer-ing and Networks Laboratory (TIK), ETH Zurich. He received his Ph.D. in2015 in the Department of Computer Science and Engineering, Hong KongUniversity of Science and Technology, under supervision of Prof. Linoel M.Ni and Prof. Yunhao Liu. He received his B.E. in 2011 in the Department ofElectronic Engineering, Tsinghua University, Beijing, China.

Lothar Thiele joined ETH Zurich, Switzerland, as a full professor ofcomputer engineering in 1994, where he currently leads the ComputerEngineering and Networks Laboratory. He received his DiplomIngenieur andDr.-Ing. degrees in Electrical Engineering from the Technical University ofMunich in 1981 and 1985 respectively. His research interests include models,methods and software tools for the design of embedded systems, embeddedsoftware and bioinspired optimization techniques. Lothar Thiele is associateeditor of IEEE Transaction on Industrial Informatics, IEEE Transactions onEvolutionary Computation, Journal of Real-Time Systems, Journal of SignalProcessing Systems, Journal of Systems Architecture, and INTEGRATION,the VLSI Journal. In 1986 he received the Dissertation Award of the TechnicalUniversity of Munich, in 1987, the Outstanding Young Author Award ofthe IEEE Circuits and Systems Society, in 1988, the Browder J. ThompsonMemorial Award of the IEEE, and in 2000/2001, the IBM Faculty PartnershipAward. In 2004, he joined the German Academy of Sciences Leopoldina. In2005, he was the recipient of the Honorary Blaise Pascal Chair of UniversityLeiden, The Netherlands. Since 2009 he is a member of the FoundationBoard of Hasler Foundation, Switzerland. Since 2010, he is a member ofthe Academia Europaea. In 2013, he joined the National Research Council ofthe Swiss National Science Foundation. Lothar Thiele received the ”EDAALifetime Achievement Award” in 2015. Since 2017, Lothar Thiele is AssociateVice President of ETH for Digital Transformation.